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How to define uniformly ticking clock defined in GR?

  1. Sep 29, 2013 #1
    I just read the following definition of a clock in GR:

    "A clock is a smooth embedding γ : t → γ(t) from a real interval into M such that the tangent vector \dot{γ} (t) is everywhere timelike with respect to g and future-pointing. This terminology is justified because we can interpret the value of the parameter t as the reading of a clock. Note that our definition of a clock does not demand that “its ticking be uniform” in any sense. Only smoothness and monotonicity are required."

    And I wondered how would a clock that is "ticking uniformly" be defined?
     
  2. jcsd
  3. Sep 29, 2013 #2

    UltrafastPED

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    Since the spacetime intervals are relativistic invariants, and on a time-like path they are non-zero - you could start by trying uniform spacetime intervals and see how they do.

    At least everybody would agree with the ticks ...
     
  4. Sep 29, 2013 #3

    DrGreg

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    Using that notation, "ticking uniformly" would mean the length of the tangent vector [itex]\dot{γ} (t)[/itex] was constant.

    The length of the tangent vector [itex]\dot{γ} (t)[/itex] is proportional to the ratio of proper time to clock time [itex]\|\dot{γ} (t)\| = c\,d\tau/dt[/itex].
     
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